Aharonov-Bohm effect in graphene Möbius strips: an analytical treatment

In this work, the influence of an Aharonov-Bohm flux on the low energy physical properties of graphene nanorings exhibiting Möbius topology is examined. Our approach lies in the continuum description of graphene, providing an analytical treatment for Aharonov-Bohm problem in the context of general relativistic confined systems, whose main goal is to understand the role of boundary conditions and their effects in such a background. We study a class of quantum rings described by a particular set of boundary conditions which combines infinite mass confinement along the transverse direction with a Möbius-type periodicity longitudinally, in order to sketch out insights into the electronic behavior of typical hard wall nanoribbons within a relativistic domain in response to the interplay between non-trivial topology and quantum interference effects. Boundary conditions are found to be only partially compatible, leading to spatial constraints on the solution, which also manifests itself in the nature of energy spectrum and persistent currents. Expressions for flux-dependent energy eigenvalues and persistent currents are explicitly calculated, as well as comparative graphs are plotted and analyzed. Both quantities are shown to alternate their expressions not only in dependence on the transverse modes, but also showing sensitivity to the allowed positions of the domain.